Fundamental Control Functions and Error Analysis in Variational Data Assimilation

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The equation for the error of the optimal solution (analysis) is derived through the errors of the input data (background and observation errors). The numerical algorithm is developed to compute the sensitivity coefficients for the analysis error using the fundamental control functions. Application to the variational data assimilation problem for a model of ocean thermodynamics is considered.